Abstract: This paper present the numerical analytical solutions for the plane wave reflection coefficient in isotropic, constant velocity medium nonuniform impedance transmission lines (with exponential, hyperbolic and linear impedance profiles). The energy efficiencies are quantified as function of v (vis the ratio of the pulse width to the one-way transit time of the transformers) and Q(Q is the ratio of the output impedance to the input impedance of the transformers).The analytical results indicate the exponential transformers have the maximum energy efficiencies when the frequency is low. Finally the energy efficiencies of Z300 are calculated, the energy efficiencies of the transmission lines with exponential, hyperbolic and linear impedance profiles are 91.%, 90.4%, 91.2% respectively.